When you right-click-->Data-->Export Features in ArcMap you get exactly what you need, a quick dropdown of all or selected features, and a quick option select to use coordinate system of source or map for the output. If you choose map's coord. system, it then uses whatever projection option you have chosen in your data frame properties to complete the export into your target shapefile.
Pro makes this process excruciating, either forcing you to pre-project a bunch of data you might not even be selecting to export, or using the environments tab on the export features dialog box and scrolling through a million coordinate systems. It doesn't even give you a nice <use data source CS> or <use map's CS> entry in the list, what the heck is that about? Then to make matters worse the transformations list is a nightmare, listing every single transformation under the sun rather than showing the predefined options between the two selected coord. systems!
Right-click export should work just like ArcMap, give the user the option to quickly select the coordinate systems and transformation settings already defined in the map's properties.